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Internal Neighbourhood Structures II: Closure and closed morphisms [PDF]
Categories and General Algebraic Structures with Applications, 2023 Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in \cite{2020}.
Partha Pratim Ghosh
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Complete Congruence Lattices of Complete Distributive Lattices [PDF]
Journal of Algebra, 1995 The authors deal with the question of whether every complete lattice \(L\) is isomorphic to the lattice of complete congruence relations of a suitable complete lattice \(K\). They prove that \(K\) can always be chosen as a complete distributive lattice. In fact, they prove a more general result: Let \(m\) be a regular cardinal \(>\aleph_ 0\). Every \(m\
Gratzer, G., Schmidt, E.T.
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On L-fuzzy ideals of multilattices [PDF]
Journal of Hyperstructures, 2023 For a given multilattice M, the set ℑM of all ideals of M is a complete lattice and for a given complete lattice L, the set FI(M;L) of all L-fuzzy ideals ofMis also a complete lattice.
Daquin Cdric Awouafack +2 more
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Set-Valued T-Translative Functions and Their Applications in Finance
Mathematics, 2021 A theory for set-valued functions is developed, which are translative with respect to a linear operator. It is shown that such functions cover a wide range of applications, from projections in Hilbert spaces, set-valued quantiles for vector-valued random
Andreas H. Hamel, Frank Heyde
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On complete congruence lattices of complete lattices [PDF]
Transactions of the American Mathematical Society, 1991 The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In this paper, we characterize this lattice as a complete lattice. In other words, for a complete latticeLL, we construct a complete latticeKKsuch thatLLis isomorphic to the lattice of complete congruence relations ofKK.
Grätzer, G., Lakser, H.
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Completely representable lattices [PDF]
Algebra universalis, 2012 It is known that a lattice is representable as a ring of sets iff the lattice is distributive. CRL is the class of bounded distributive lattices (DLs) which have representations preserving arbitrary joins and meets. jCRL is the class of DLs which have representations preserving arbitrary joins, mCRL is the class of DLs which have representations ...
Egrot, R, Hirsch, R
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“Complete-simple” distributive lattices [PDF]
Proceedings of the American Mathematical Society, 1993 It is well known that the only simple distributive lattice is the two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences. In this paper we show the existence of infinite complete-simple distributive lattices.
Grätzer, G., Schmidt, E. T.
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Non-deterministic-M-fuzzy Lattices
Ratio Mathematica, 2023 Goran Trajakoviski and Tepavcevic´invented the L-fuzzy lattice in which a ´ bounded lattice is fuzzified using a complete lattice. Using a complete consistent distributive multilattice M, we broaden the concept of L-fuzzy lattice to Nd-M-fuzzy lattice ...
Gireesan K.K. +2 more
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Equalizers and Coequalizers in the Category of Topological Molecular Lattices [PDF]
Journal of Mahani Mathematical Research, 2023 A completely distributive complete lattice is called a molecular lattice. It is well known that the category TML of all topological molecular lattices with generalized order homomorphisms in the sense of Wang, is both complete and cocomplete.
Ghasem Mirhosseinkhani, Narges Nazari
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Fuzzy Initial and Final Segments in ADL’s
International Journal of Analysis and Applications, 2023 In this paper, we define the concepts of fuzzy initial and final segments in an Almost Distributive Lattice (ADL) and certain properties of these are discussed. It is proved that the set of fuzzy initial segments forms a complete lattice and that the set
G. Srikanya +3 more
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